The purpose of this project is to conduct research in mathematical statistics, probability, and applied mathematics in order to develop new statistical methodology applicable to biomedical sciences. We are investigating new approaches for displaying temporal trends in rates in cancer maps and for quantifying the impact of SES on cancer risk using U.S. county mortality rates. We continue research into methods for designing epidemiologic studies with maximum power for equivalence testing, and have developed efficient methods for matched-pair designs. We also derived formulas for determining power and sample size requirements for equivalence testing based on the rate ratio estimated from matched samples and are investigating methods for testing equivalence with censored survival data. We investigated methods of assessing inter-rater agreement, and derived an efficient confidence interval estimate for the kappa coefficient. We are continuing to investigate optimal methods for estimating the attributable risk, or etiologic fraction, and for calculating confidence intervals which correct for the negative bias in most current methods. We also continue investigations into methods for examining birth cohort and calendar period trends in disease rates, continuing a simulation study of the performance of two novel, exact permutation tests for changes in the slope of the birth cohort trend. A computer program to implement the exact non-parametric methods for examining birth cohort trends is being improved, and development continues on a computer program implementing parametric methods for examining birth cohort and calendar period patterns of risk in age-period-cohort models. We continue developing methods for examining mutational spectra in a defined DNA sequence, including tests for whether a certain pattern of mutations occurs more frequently than expected by chance in a specific gene. We developed methods for estimating the concordance between laterality of cancer and laterality of exposure, for use in evaluating the possible association between cell phone use and brain cancer.